Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
91
A Modeling Framework of Supply Chain Simulation
Beom-cheol Park Kwangwoon University, Seoul, Korea
Sukjae Jeong* Kwangwoon University, Seoul, Korea
To satisfy and respond quickly to customer’s demands, many companies are now aggressively
focusing on supply chain management in order to strengthen their competitiveness. Thus, the
modeling and analysis of supply chain environment have been widely studied for the better
management of supply chain functions. This study is to develop a supply chain simulator that deals
with stochastic characteristics of the supply chain environment. We propose a mathematical model
for an efficient cost analysis and present a supply chain simulator in an object-oriented language
C++ based on the proposed mathematical model. A simple experiment is conducted to show the
usefulness and applicability of the developed simulator.
* Corresponding Author. E-mail address: [email protected]
I. INTRODUCTION
With the increasing interest in supply
chain management (SCM), most companies are
speeding up to develop a solution that can
efficiently support SCM. From an operational
perspective, SCM is to effectively integrate
supplier, manufacturers, warehouses, and stores,
so that products are produced and distributed at
the right quantities, to the right locations, and at
the right time, in order to minimize system wide
cost while satisfying service requirements.
However, it is not easy to coordinate the
operations of individual supply chain members
and improve system profit (Ganeshan et al.,
2000).
The modeling and analysis of supply
chain environment have been active research
agenda in the SCM field for many years. Vidal
and Goetschalckx (1997) reviewed the strategic
production-distribution model. They focused
on global supply chain models with emphasis
on mixed integer programming models.
Petrovic et al. (1999) described fuzzy modeling
and simulation of a supply chain in an uncertain
environment. Lee and Kim (2002) obtained
more realistic optimal production-distribution
plans for the integrated supply chain system
reflecting stochastic natures by using iterative
simulation procedures. Thomas and Griffin
(1996) developed supply chain models to
support both strategic supply chain planning
and operations control of the supply chain
activities. Cohen and Lee (1988) represented
mathematical models that consider the whole
supply chain networks.
However, the existing mathematical
models could not represent the stochastic
properties of the supply chain. Simulation is an
effective analysis tool for dynamically
changing environments of internal supply
chains. Moreover, simulation can be used to
achieve an optimization of planning an entire
supply chain system (Lee et al., 2002).
Industry has promoted the development
of simulators for supply chain system analyses.
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
92
IBM developed SCA (Supply Chain Analyzer)
based on Simprocess and provided inventory
optimizer and supply planning (Bagchi et al,
1999). Also, Compaq developed CSCAT
(Compaq Supply Chain Analyzer Tool) based
on Arena. Nokia developed LOGSIM based on
ProModel. LOGSIM consists of the five
components - supplier, buffer, production and
assembly process, customer, material
requirement planning. In this paper, we
developed an integrated simulator supporting
multi-periods, multi-products, multi-facilities
production and distribution model in supply
chain environment.
This study developed a supply chain
simulator which can reflect stochastic
phenomena of supply chain activities into the
modelling and analyses of a supply chain
system. The characteristics of complex
problems in SCM are defined in a mathematical
model, and then a supply chain system is
analysed by using the simulator. This paper is
organized as follows: In chapter 2, a
mathematical model that can support decision
making is proposed. In chapter 3, a supply chain
simulator developed using the mathematical
model is introduced. In chapter 4, experiments
and results for the developed simulator are
shown. Concluding remarks are provided in
chapter 5.
II. MATHEMATICAL MODEL
We present a comprehensive
mathematical model that can support a supply
chain simulator to be presented in the next
section. The model is consisted of supplier,
factory, DC (distribution center), customer, and
transport stages in order to help the efficient
cost analysis.
Indices
i : number of raw materials ( i = 1, 2,
… , i )
p : number of products ( p = 1, 2, …, p )
t : number of periods ( t=1, 2, …, t )
s : number of suppliers ( s = 1, 2, …, s )
f : number of factories ( f = 1, 2, …, f )
d : number of distribution centers (d = 1,
2, …, d )
c : number of customers ( c = 1, 2, …,
c )
Parameters
Ss : fixed cost at supplier s
Sf : fixed cost at factory f
Sd : fixed cost at DC d
Sc : fixed cost at customer c
MS : maintenance cost at suppler s
Mf : maintenance cost at factory f
Md : maintenance cost at DC d
Mc : maintenance cost at customer c
Zs : 1, if production takes place at
supplier s,
: 0, otherwise
Zf : 1, if production tacks place at
factory f
: 0, otherwise
Zd : 1, if DC d is opened
: 0, otherwise
Zc : 1, if customer c is opened
: 0, otherwise
Ptis : production amount of raw material
i at supplier s during period t
Ptpf : production amount of product p at
factory during period t
Ptif : input amount of Material i at
factory f during period t
CPis : unit cost of producing of raw
material i at supplier s
CPpf : unit cost of producing of product
p at factory f
Ttisf : transportation amount of raw
material i at supplier s to factory f
during period t
Ttpfc : transportation amount of product
p at factory f to customer c during
period t
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
93
Ttpfd : transportation amount of product
p at factory f to DC d during period
t
Ttpdc : transportation amount of product
p at DC d to customer c during
period t
CTisf : unit cost of transportation from
supplier s to factory f
CTpfd : unit cost of transportation from
factory f to DC d
CTpdc : unit cost of transportation from
DC d to customer c
Itis : inventory amount of raw material
i at supplier s during period t
Itif : inventory amount of raw material
i at factory f during period t
Itpf : inventory amount of product p at
factory f during period t
Itpd : inventory amount of product p at
DC d during period t
his : unit cost of inventory of source i
at supplier s
hif : unit cost of inventory of source i
at factory f
hpf : unit cost of inventory of product p
at factory f
hpd : unit cost of inventory of product p
at DC d
Btifs : demand of raw material i at factory
f to supplier s during period t
Btpdf : demand of product p at DC d to
factory f during period t
Btpcd : demand of product p at customer
c to DC d during period t
CBifs : unit cost of demanding of raw
material i at factory f to supplier s
CBpdf : unit cost of demanding of product
p at DC d to factory f
CBpcd : unit cost of demanding of product
p at customer c to DC d
Kpd : capacity of product p at DC d
TK : capacity of all DCs
Supplier stage
t i s s
SSis
t
is ZShIzmin
t i s s
SSis
t
is ZMCPP
. . ts (1) ,, 1 tsiITPI
f
t
is
t
isf
t
is
t
is
(2) }1,0{ sZS
(3) , , 0 , , tsiTPI tisft
is
t
is
The objective function in the supplier
stage is to minimize the sum of production cost,
inventory cost, maintenance cost, and fixed cost
of raw materials. Constraint (1) represents
inventory balanced equations that define the
inventory levels at the end of period t at supplier
stage resulting from the production and
transportation. Constraint (2) is the binary
variable to decide whether or not that each
supplier can be operated.
Factory stage
t p f f
ff
t i f
if
t
ifpf
t
pf ZShIhIz min
t i f s
ifs
t
ifs
t p f
pf
t
pf
f
ff CBBCPPZM
. . ts (4) ,,, tsfiTB
f
t
isf
t
ifs
(5) ,, 1 tfpITPId
t
pf
t
pfd
t
pf
t
pf
(6) ,,, 1 tsfiIPTI tif
t
if
t
isf
t
if
(7) }1,0{ fZ f
(8) , ,,, , 0 ,, , , tspfdiTTBII tpfdt
isf
t
ifs
t
pf
t
if
The objective function in the factory
stage is to minimize the sum of fixed cost,
maintenance cost, inventory cost of raw
material and product, production cost, and
purchase cost. Constraint (4) means that all
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
94
demands of raw materials from each factory
must be equal to the transportation amount of
the raw materials to the factory. Constraint (5)
is the equation related to the inventory of
product during period t. Constraint (6) is the
equation related to the inventory of raw
material. Constraint (7) is the binary variable
for deciding whether open or not at each factory.
Distribution Center stage
t d p d
ddpd
t
pd ZShIzmin
t p c d
t
d
dd CBBZM
. . ts (9) ,,, tpfdTB
f
t
t
(10) ,,, 1 tpdcITIc
t
pdc
t
pdc
t
pd
(11) ,, tpdKTp
pd
c
t
pdc
(12) dKTkp
pd
(13) }1,0{ dZd
(14) ,,,, , 0 ,, , tpifdcTTBI tpdft
pcd
t
t
if
The objective function of the DC stage
is to minimize the sum of fixed cost,
maintenance cost, inventory cost, and purchase
cost. Constraint (9) means that all demands of
DC must be equal to the amount of
transportation. Constraint (10) is the equation
related to the inventory of products at DC
during period t. Constraint (11) prevents the
transportation amount of product p at DC d
from exceeding its storage capacity at the DC.
Constraint (12) means that total capacity must
be bigger than the sum of each. Constraint (13)
is the binary variable.
Customer stage
t p c d
pcd
t
pcd
c
cc
c
cc CBBZMZSzmin
. . ts (15) ,,, tpdcTB
c
t
pcd
t
pcd
(16) }1,0{ cZc
(17) ,, , 0 , tpdcTB tpcdt
pcd
At customer stage, the objective
function is to minimize the sum of fixed cost,
maintenance cost, and purchase cost. Constraint
(15) means that all demands of customer must
be equal to the amount of transportation.
Transport stage
. . ts
(18) ,,,,, , 0 , , , tspifdcTTTT tpfct
pcd
t
t
isf
The objective function of transport
stage is to minimize the sum of transport cost to
factory, to DC, and to customer. It can be
defined as the optimal mathematical equation
that minimizes the inventory cost, production
and transportation cost, fixed cost, and
maintenance cost.
III. SUPPLY CHAIN SIMULATOR
There are many uncertain variables with
stochastic property in a supply chain
environment. It is not easy to find an optimal
solution with the existing analytical methods
like LP (Linear Programming) and DP
(Dynamic Programming). However, simulation
is known as the most efficient method for
t p d c
pdc
t
pdc
t p f d
pfd
t
pfd
t p f d
t
t i s f
isf
t
isf CTTCTTCTTCTTzmin
t p d c
pdc
t
pdc
t p f d
pfd
t
pfd
t p f d
t
t i s f
isf
t
isf CTTCTTCTTCTTzmin
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
95
dealing with stochastic variables existing
within the supply chain environment. The
supply chain simulation which could represent
an overall supply chain system with
mathematical model is efficient in finding
solutions under many constraints, and reflects
all the uncertainties existing in a supply chain
system such as the demand of customers,
delivery time of products and raw materials,
and service rates for customers.
We developed a supply chain simulator
usin object-oriented modeling. The most
important reason for the widespread appeal of
object oriented modeling is the natural mapping
paradigm. This allows one to one mapping
among objects, which is the abstraction
standing for a real-world entities in the system.
Object-oriented modeling also affects
simulation implementation through its
facilitation of modular design and software
reusability.
3.1. Simulation Internal Process
3.1.1. Event
An event is defined as something that
happens at an instant of simulated time. The
event has information such as time, object,
production and transportation volume, priority
and due date. An event function is defined as
something that processes the information of
event. The event function is activated by the
event during simulated time. The event
functions are consisted of order-arrival function,
process function, production function,
inventory function, and transport function
according to each object. The simulator engine
consists of event function, event calendar, event
creation function, output function. Fig. 1 shows
the engine of the simulation.
FIGURE 1. THE OVERVIEW OF THE SIMULATOR ENGINE
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
96
FIGURE 2. THE TAXONOMY OF OBJECTS MODEL IN SUPPLY CHAIN
3.1.2. Objects Model of Supply Chain
Fig. 2 shows the classes representing the
taxonomy of objects model in supply chain. The
developed simulator consists of the external
objects like customer, DC, factory, supplier and
internal object like the common object.
3.1.2.1. Internal Object
A common object has common
information for external objects, which play a
role of mutually exchanging information of
individual objects.
Input data of common object
■ Product and Material
Input data of common object are commonly
used in factory, DC and supplier.
Unit Cost of
Inventory - input data for unit cost of raw material and product
Virtual Inventory - product and raw material producing during any given period
Real Inventory - the inventory of raw material and product during any given period
Order Policy - order policy for each product and raw material
Order Point
- reorder point for raw material and product
(r,Q) or (r,S) policy : reorder point
(s,S) policy : reorder point inspection cycle
Order Volume
- order quantity at reorder point
(r,Q) policy : order quantity
(s,S) policy : target inventory
Lot Order Size - information for lot size of ordering
Unit Cost of Order - input data for unit cost of order
Call Delay - the time taken for ordering raw material and product
Capacity - capacity for raw material and product
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
97
Function of common object
■ Delay (Inbound Delay, Outbound Delay)
Delay is a function for calculating delay
time. The delay consists of Inbound Delay and
Outbound Delay function. It can select various
probability distributions (Exponential, Uniform,
Normal, Gamma, Beta, Binomial, Geometric,
and Hypergeometric Distribution) to consider
the stochastic property in supply chain
environment
3.1.2.2. External Objects
External objects are consisted of
supplier, factory, distribution center and
transport object. The roles of each object are as
follows.
Supplier object
The input data of supplier object are
consisted of production policy that determines
production of raw materials, setup time,
production time per lot size and delay time of
outbound. The function of supplier object is
consisted of order arrival function, order
processing function, production function of raw
materials and inventory function.
The procedure of the order process in
supplier object is listed as:
Step 1 : Orders from factory object arrive.
Step 2 : Check the amount of real inventory to
satisfy orders.
Step 3 : If satisfies, the order process is started
immediately.
Otherwise, check the virtual inventory.
Step 4 : If the virtual inventory satisfies orders,
the order process is started.
Otherwise, produce according to
production plans generated in supplier
object.
Fig 3 shows the order process occurred
in supplier object.
FIGURE 3. THE PROCEDURE OF THE ORDER PROCESS IN SUPPLIER OBJECT
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
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FIGURE 4. THE PROCEDURE OF THE ORDER PROCESS IN FACTORY OBJECT
FIGURE 5. THE PROCEDURE OF THE PRODUCTION PROCESS
IN FACTORY OBJECT
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
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Factory object
The input data of factory object are
consisted of production policy that determines
production of product, setup time, production
time per lot size and delay time of inbound and
outbound. The function of factory object is
consisted of order arrival function, order
processing function, production function of
product and inventory function of raw material
and product.
The procedure of the order process in
factory object is listed as:
Step 1 : Orders from DC objects arrive
Step 2 : Check the amount of real inventory to
satisfy orders
Step 3 : If satisfies, the order process is started
immediately.
Otherwise, check the virtual inventory.
Step 4: If the virtual inventory satisfies orders,
the order process is started.
Otherwise, produce according to
production plans generated in factory
objects.
Fig 4 and 5 show the order process
occurred in factory object.
DC object
The input data of DC object are
consisted of the order policy that determine the
order planning, and delay time of inbound and
outbound. The function of DC object is
consisted of order arrival function, order
processing function and inventory function.
The procedure of the order process in
DC object is listed as:
Step 1 : Orders from customer objects arrive
Step 2 : Check the amount of real inventory to
satisfy orders.
Step 3 : If satisfies, the order process is started
immediately.
Otherwise, check the virtual inventory.
Step 4 : If the virtual inventory satisfies orders,
the order process is started.
Otherwise, generate orders to factories.
Fig 6 shows the order process occurred
in DC object.
FIGURE 6. THE PROCEDURE OF THE ORDER PROCESS IN DC OBJECT
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
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FIGURE 7. THE PROCEDURE OF THE TRANSPORTATION PROCESS
IN TRANSPORT OBJECT
FIGURE 8. THE ARCHITECTURE OF INTEGRATED SCM SIMULATOR
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
101
Customer object
The input data of customer object are
consisted the amount of order and order time.
The function of customer object is consisted of
the initial order function and order arrival
function.
Transport object
The input data of transport object are
consisted of location that indicates location
information for all external objects and
transportation time between all external objects.
The function of transport object is consisted of
the initial order function that generates orders
firstly and order arrival function.
Fig. 8 shows the architecture of
integrated supply chain simulator which
includes the simulation engine, internal and
external objects.
3.2. Inventory Replenishment Policy
The inventory replenishment policy
determines when an object will generate a
replenishment order to restock its capacities.
The developed simulator is applied to the policy
of production and order.
BTO (Build to Order) policy
The build-to-order policy maintains a
minimum inventory. The object generates a
replenishment order only if a customer order
arrives and product is not available to fill the
order. The replenishment order requests only
the amount of the product needed to satisfy the
customer order.
BTP (Build to Plan) policy
Replenishment orders are issued
according to production plans generated by the
developed simulator.
Continuous review policy
The object generates a replenishment
order every time the inventory level falls below
its reorder point.
Periodic review policy
This policy is controlled by a periodic
review policy instead of a continuous review
policy. The Periodic means that the inventory
position is inspected at the beginning of each
period. The object generates a replenishment
order only when the inventory level is below its
reorder point.
FIGURE 9. THE SCENARIO FOR SUPPLY CHAIN MODEL
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
102
IV. EXPERIMENT AND RESULT
Computational experiments have been
provided in order to demonstrate the
effectiveness and reasonability of the
developed simulator. For the experiment of the
developed simulator, two-echelon supply chain
model was designed
4.1. Scenario for Experiment
The conditions for the experiments are
given as follows. The number of each external
object in the supply chain model was 2
respectively, and product and raw material were
also 2. The number of order at customer C0 was
3, and C1 was 1, and initial and virtual
inventories were randomly given at each DC
and factory. Inbound and Outbound time,
production time and order time were also
randomly given. Simulation time was set at
10000.
4.2. Input Data
TABLE 1. CUSTOMER ORDER TABLE 2. DC INPUT DATA
From To Product No. of
Order
Order
Interval
Due
date Priority
DC1 AAA BBB
Total
Capacity
C0 D0 AAA 30 Exp(500) 300 1 Virtual
Inv. 40 50
C0 D0 BBB 30 300 50 1 Real
Inv. 40 50
C0 D1 BBB Unif
(50,70) 400 200 2
Reorder
Point 20 20
C1 D1 AAA 40 200 100 3 Quantity 100 80
Capacity 150 100 200
TABLE 3. FACTORY INPUT DATA TABLE 4. SUPPLIER INPUT DATA
Product AAA BBB Raw
material aaa bbb
Material aaa bbb
Virtual
Inv. 80 100
Virtual
Inv. 40 50
Virtual
Inv. 480 600
Real
Inv. 80 100
Real
Inv. 40 50
Real
Inv. 480 600
Reorder
Point 40 40
Reorder
Point 20 20
Reorder
Point 240 240
Quantity 200 160 Quantity 100 80 Quantity 1200 960
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
103
4.3. Output Results
The result of the experiment is shown as follows.
TABLE 5. CUSTOMER ORDER OUTPUT
Customer DC Product No. of
Order
Quantity
of Order
No. of
Arrival
Quantity
Of Arrival
Arrival in
Due date
Service
Rate
C0 D0 AAA 25 750 4 120 120 100.0
C0 D0 BBB 34 1020 6 180 150 83.3
C0 D1 AAA 26 1571 6 383 383 100.0
C1 D1 BBB 51 2040 3 120 120 100.0
TABLE 6. DC ORDER OUTPUT
DC Factory Product No. of
Order
Quantity
of Order
No. of
Arrival
Quantity
of Arrival
Arrival in
Due date
Service
Rate
D0 F0 AAA 3 210 2 110 110 100.0
D0 F0 BBB 4 250 0 0 0 0
D0 F1 BBB 1 170 3 170 170 100.0
D1 F0 BBB 6 433 4 383 383 100.0
D1 F1 AAA 3 220 2 120 120 100.0
TABLE 7. DC DELIVERY OUTPUT
DC Customer Product No. of
Delivery
Quantity
of Delivery
Arrival
in due date
Service
Rate
D0 C0 AAA 4 120 120 100.0
D0 C0 BBB 6 180 150 100.0
D1 C0 BBB 6 383 383 100.0
D1 C1 AAA 3 120 120 100.0
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
104
TABLE 8. FACTORY ORDER OUTPUT
Factory Supplier Raw
material
No. of
Order
Quantity
of Order
No. of
Arrival
Quantity
of
Arrival
Arrival in
due date
Service
Rate
F0 S0 aaa 2 120 1 600 600 100.0
F0 S1 bbb 3 1440 2 960 960 100.0
F1 S0 bbb 2 960 2 960 480 50.0
F1 S1 aaa 1 320 1 320 0 0
TABLE 9. FACTORY DELIVERY OUTPUT
Factory DC Product No. of
Delivery
Quantity pf
Delivery
Arrival in
due date
Service
Rate
F0 D0 AAA 2 110 110 100.0
F0 D1 BBB 4 383 383 100.0
F1 D0 BBB 3 170 90 52.9
F1 D1 AAA 2 120 120 100.0
TABLE 10. FACTORY PRODUCTION OUTPUT
Factory Product No. of
Production
Quantity
of Delivery
F0 AAA 2 200
F0 BBB 4 700
F1 AAA 3 200
F1 BBB 3 320
TABLE 11. SUPPLIER DELIVERY OUTPUT
Supplier Factory Raw
material
No. of
Delivery
Quantity
of Delivery
Arrival
in due date
Service
Rate
F0 D0 aaa 1 600 600 100.0
F0 D1 bbb 2 960 480 50.0
F1 D0 bbb 2 960 960 100.0
F1 D1 aaa 1 320 0 0
Beom-cheol Park, Sukjae Jeong A Modeling Framework of Supply Chain Simulation
Journal of Supply Chain and Operations Management, Volume 12, Number 2, May 2014
105
TABLE 12. SUPPLIER PRODUCTION OUTPUT
Supplier Raw
material
Num of
Production
Quantity
of Delivery
S0 aaa 2 1200
S0 bbb 2 960
S1 aaa 0 0
S1 bbb 3 960
V. CONCLUSION
The mathematical modeling and
analytical method of supply chain environment
have been widely studied. However, existing
analytical method could not cover all variables
with stochastic properties in the supply chain
environment. We have developed a supply
chain simulator which considers the stochastic
property. Also, we proposed the mathematical
model for the cost analysis for supply chain
activities. A simple experiment was done to
show the benefits of the developed simulator.
For further research, it is necessary to
develop the simulator for generating graphical
output data such that decision makers can see
how the supply chain acts over time during
simulation.
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